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    "# 光电效应中遏止电压与入射光波长的关系\n",
    "\n",
    "## 核心结论\n",
    "\n",
    "**遏止电压 ($U_c$) 与入射光波长 ($\\lambda$) 成反比关系。** 波长越长（频率越低），对应的遏止电压越小；当波长超过截止波长 ($\\lambda_c$) 时，遏止电压降至零，不再发生光电效应。\n",
    "\n",
    "---\n",
    "\n",
    "## 1. 物理公式推导\n",
    "\n",
    "该关系由爱因斯坦光电效应方程和遏止电压定义共同推导得出。\n",
    "\n",
    "### 基本公式\n",
    "1.  **光电效应方程**：\n",
    "    $$ h\\nu = W_0 + E_{k,\\max} $$\n",
    "    *   $h$：普朗克常数\n",
    "    *   $\\nu$：入射光频率\n",
    "    *   $W_0$：阴极材料的逸出功\n",
    "    *   $E_{k,\\max}$：光电子最大初动能\n",
    "\n",
    "2.  **遏止电压定义**：\n",
    "    $$ E_{k,\\max} = e U_c $$\n",
    "    *   $e$：元电荷\n",
    "    *   $U_c$：遏止电压\n",
    "\n",
    "3.  **频率与波长关系**：\n",
    "    $$ \\nu = \\frac{c}{\\lambda} $$\n",
    "    *   $c$：真空光速\n",
    "    *   $\\lambda$：入射光波长\n",
    "\n",
    "### 最终关系式\n",
    "将上述公式结合，得到 $U_c$ 与 $\\lambda$ 的直接关系：\n",
    "\n",
    "$$ h \\frac{c}{\\lambda} = W_0 + e U_c $$\n",
    "\n",
    "$$ e U_c = \\frac{hc}{\\lambda} - W_0 $$\n",
    "\n",
    "$$ \\boxed{U_c = \\frac{hc}{e} \\cdot \\frac{1}{\\lambda} - \\frac{W_0}{e}} $$\n",
    "\n",
    "此公式表明 $U_c$ 是 $(1/\\lambda)$ 的**线性函数**。\n"
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